Chapter 2.2, Problem 7E

Let A = $\left[\begin{array}{cc}1& 2\\ 5& 12\end{array}\right]$, b₁ = $\left[\begin{array}{c}-1\\ 3\end{array}\right]$, b₂ = $\left[\begin{array}{c}1\\ -5\end{array}\right]$, b₃ = $\left[\begin{array}{c}2\\ 6\end{array}\right]$, and b₄ = $\left[\begin{array}{c}3\\ 5\end{array}\right]$.

1. a. Find A⁻¹, and use it to solve the four equations Ax = b₁, Ax = b₂, Ax = b₃. Ax = b₄
2. b. The four equations in part (a) can be solved by the same set of row operations, since the coefficient matrix is the same in each case. Solve the four equations in part (a) by row reducing the augmented matrix [A b₁ b₂ b₃ b₄].